Question

Four particles, each of mass 1 kg, are placed at the corners of a square of side 1m in the X-Y plane. If the point of intersection of the diagonals of the square, is taken as the origin the coordinates of the centre of mass are

• A. (1, 1)
• B. (-1, 1)
• C. (1, -1)
• D. (0, 0)

Answer 1

Answer: (D)

Given, $m_1=m_2=m_3=m_4=1kg$ $AB=BC=CD=DA=1m$
Hence, the coordinates of A,B, C, D, are given in the figure from the relation for $x_{cm}$ is $x_{cm}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3+m_4{x}_4}{m_1+m_2+m_3+m_4}$ $=\frac{1\times 0.5+1\times 0.5+1(-0.5)+1\times (-0.5)}{1+1+1+1}=0$ $y_{cm}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3+m_4{y}_4}{m_1+m_2+m_3+m_4}$ $=\frac{1\times 0.5+1\times (-0.5)+1\times (-0.5)+1\times (0.5)}{1+1+1+1}$ $=0$